Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence

TL;DR

This work tackles the challenge of large-$N$ volume independence in Yang-Mills theory by introducing a simple double-trace deformation that stabilizes center symmetry at arbitrarily small volumes, making the deformed theory equivalent to ordinary YM up to $O(1/N^2)$ corrections. It develops a controllable analytic regime for small circle size $L$, where confinement and a mass gap arise from a dilute monopole plasma, described by a dual three-dimensional theory with $N$ monopole types and a mass gap for the photons. The authors establish large-$N$ equivalence and volume independence between ordinary and deformed YM through Schwinger-Dyson loop equations, extend the construction to multiple compact dimensions and to QCD-like theories, and analyze the behavior of string tensions, monopole dynamics, and connections to affine Toda theory. The framework yields a fully reduced matrix-model perspective and provides analytic insight into confinement in a purely gauge theory without extra scalars or supersymmetry, with potential applications to lattice studies and QCD-like theories.

Abstract

We examine a double trace deformation of SU(N) Yang-Mills theory which, for large $N$ and large volume, is equivalent to unmodified Yang-Mills theory up to $O(1/N^2)$ corrections. In contrast to the unmodified theory, large $N$ volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which would otherwise disrupt large $N$ volume independence in small volumes. For small values of $N$, if the theory is formulated on $\R^3 \times S^1$ with a sufficiently small compactification size $L$, then an analytic treatment of the non-perturbative dynamics of the deformed theory is possible. In this regime, we show that the deformed Yang-Mills theory has a mass gap and exhibits linear confinement. Increasing the circumference $L$ or number of colors $N$ decreases the separation of scales on which the analytic treatment relies. However, there are no order parameters which distinguish the small and large radius regimes. Consequently, for small $N$ the deformed theory provides a novel example of a locally four-dimensional pure gauge theory in which one has analytic control over confinement, while for large $N$ it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories.